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Topological relationships between spatial objects have been a focus of research on spatial data handling and reasoning for a long time. Especially as predicates they support the design of suitable query languages for spatial data retrieval and analysis in databases. Unfortunately, they are so far only applicable to simplified abstractions of spatial objects like single points, continuous lines, and simple regions, as they occur in systems like current geographical information systems and spatial database systems. Since these abstractions are usually not sufficient to cope with the complexity of geographic reality, their generalization is needed which especially has influence on the nature, definition, and number of their topological relationships. This paper partially closes this gap and first introduces very general spatial data types for complex points and complex regions. It then defines the corresponding complete sets of mutually exclusive, topological relationships.